Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows
1Department of Chemical and Biomolecular Engineering, Sogang University, Seoul, South Korea. hmpark@sogang.ac.kr
Journal of Colloid and Interface Science
|October 16, 2007
Summary
A new, simple method accurately predicts the volumetric flow rate of viscoelastic electroosmotic flows in microchannels. This approach adapts the Helmholtz-Smoluchowski velocity, simplifying complex fluid dynamics calculations.
Area of Science:
- Fluid Dynamics
- Biophysics
- Microfluidics
Background:
- Biofluids like blood and DNA solutions exhibit complex viscoelastic properties, deviating from simple Newtonian fluid behavior.
- Modeling these viscoelastic flows, especially electroosmotic flows in microchannels, presents significant computational challenges due to rapid velocity gradients near surfaces.
Purpose of the Study:
- To develop a simplified method for calculating the volumetric flow rate of viscoelastic electroosmotic flows.
- To adapt the established Helmholtz-Smoluchowski velocity concept for non-Newtonian fluids in microfluidic devices.
Main Methods:
- The study employs a simplified approach based on the Helmholtz-Smoluchowski velocity, traditionally used for Newtonian fluids.
- This method involves solving a straightforward cubic algebraic equation to determine the modified velocity for viscoelastic fluids.
Main Results:
- The proposed method successfully determines the Helmholtz-Smoluchowski velocity for viscoelastic fluids.
- Volumetric flow rates calculated using this simplified method closely match those obtained from solving complex governing partial differential equations.
Conclusions:
- A computationally efficient and accurate method for predicting viscoelastic electroosmotic flow rates in microchannels has been established.
- This technique offers a practical alternative to complex numerical simulations for microfluidic applications involving biofluids.
Related Concept Videos
01:27Viscosity
Viscosity is a property of fluids that measures their resistance to flow. It is influenced by factors such as the surface area of contact, the gradient of flow speed, and the fluid's viscosity constant, called the coefficient of viscosity. The coefficient of viscosity, also known as dynamic viscosity, is denoted by the symbol η. It determines the proportionality between the viscous force and the gradient of flow speed.Newton's law of viscosity states that the viscous force on a faster-moving...
01:17Viscosity
When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
The SI unit of viscosity is...
The SI unit of viscosity is...
01:28Euler's Equations of Motion
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
01:18Newtonian Fluid: Problem Solving
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
01:19Viscosity of Fluid
Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
01:28Navier–Stokes Equations
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...